Hostname: page-component-7dd5485656-pnlb5 Total loading time: 0.001 Render date: 2025-10-31T06:09:39.615Z Has data issue: false hasContentIssue false
  • English
  • Français

Determination of phase velocities of a circular helix using the method of internal constraints

Published online by Cambridge University Press:  24 October 2008

J. W. Lincoln ,
M. Nikkhah  and
E. Volterra
J. W. Lincoln
Affiliation:
L.T.V. Aerospace Corporation, Dallas, Texas TheUniversity of Texas at Austin, Texas, U.S.A.
M. Nikkhah
Affiliation:
L.T.V. Aerospace Corporation, Dallas, Texas TheUniversity of Texas at Austin, Texas, U.S.A.
E. Volterra
Affiliation:
L.T.V. Aerospace Corporation, Dallas, Texas TheUniversity of Texas at Austin, Texas, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

A procedure is described to determine phase velocities of a circular helix. Computations are made for three helix configurations using the method of internal constraints. The results so obtained are compared with the results obtained by using the elementary theory proposed by J. H. Michell, and the extended elementary theory proposed by A. B. Basset.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 2 , March 1970 , pp. 509 - 521
Copyright
Copyright © Cambridge Philosophical Society 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1)Michell, J. H.The small deformation of curves and surfaces with application to the vibrations of a helix and a circular ring. Messenger of Mathematics 19 (1890), 68–82.Google Scholar
(2)Basset, A. B.On the theory of elastic wires. Proc. London Math. Soc. 23 (1892), 105–127.Google Scholar
(3)Love, A. E. H.The propagation of waves of elastic displacement along a helical wire. Trans. Cambridge Philos. Soc. 18 (1900), 364–374.Google Scholar
(4)Volterra, E.Elastidtd Libera ed. Elasticita Vincolata. Applicazioni del Concetto di Elasticitd Vincolata, Proceedings of the International Congress of Mathematics. (Zurich 1932), vol. 2, pp. 247–248.Google Scholar
(5)Volterra, E.Elasticita vincolata e sua schematizzazione matematica. Rendiconti delta Reale Accademia Nazionale dei Lincei, vol. xvi, Ser. 6, Fase. 5–6, (1932), pp. 220–222.Google Scholar
(6)Nature, 21 01 1933, p. 107.Google Scholar
(7)Volterra, E.A one-dimensional theory of wave-propagation in elastic rods based on the method of internal constraints. Ing.-Arch. 23 (1955), 410–420.CrossRefGoogle Scholar
(8)Volterra, E.Second approximation of Method of internal constraints and its applications. Internal. J. Mech. Sci. 3 (1961), 47–67.CrossRefGoogle Scholar
(9)Volterra, E. and Zachmanoglou, E. C.Dynamics of vibrations, Chapters iv and vi, Columbus (Ohio, 1956).Google Scholar
(10)Volterra, E.Some recent progress in vibrations, General Lecture Proceedings of the Tenth Midwestern Mechanics Conference, Developments in Mechanics, vol. 4, pp. 1–13.Google Scholar
(11)Lincoln, J. W. and Volterra, B.Experimental and theoretical determination of frequencies of elastic toroids. Experimental mechanics 7 (1967), 211–217.CrossRefGoogle Scholar
(12)Ainola, L. and Nigul, U.Stress waves in elastic plates and shells (in Russian). Izv. Ahad. Nauk. Estonskoi SSR, 14 (1965), 1–63. (Available at Technical Information Service, Amer. Inst. of Aeronautics, New York, (U.S.A.).)Google Scholar
(13)Levi-Civita, T.The absolute differential calculus (London, 1926).Google Scholar
(14)Timoshenko, S.On the correction for shear of the differential equations for transverse vibrations of prismatic bars. Philos. Mag. Series 6, 41 (1921), 744–746.CrossRefGoogle Scholar
(15)Timoshenko, S.On the transverse vibrations of bais of uniform cross section. Philos. Mag., Series 6, 43 (1922), 125–131.CrossRefGoogle Scholar
(16)Pochhammer, L.Uber Fortpflanzungsgeschwindigkeiten Kleiner Schwingungen in Einem Unbegrenzten Isotropen Kreiszylinder. Zeitschrift fur die reine und angewandte Mathematik (Crelle) 81 (1876), 324–336.Google Scholar
(17)Chree, C.The equations of an isotropic elastic solid in polar and cylindrical coordinates, their solution and application. Trans. Cambridge Philos. Soc. 14 (1889), 588–593.Google Scholar